1. Field
The present disclosure is directed to a method and apparatus for optimizing antenna precoder selection with coupled antennas.
2. Introduction
The precoding matrices defined in the 3rd Generation Partnership Project (3GPP) wireless communication protocols and elsewhere are generally believed to yield a set of antenna patterns having equal energy. However, there is a contradiction in the specification in that if the precoding matrices are applied in a way that the resulting antenna patterns are equal in energy, the precoding matrix-based channel estimates used for demodulation, precoding matrix selection, and channel quality estimation will have scaling error. Furthermore, the scaling error will be a function of the precoding matrix. Conversely, if the precoding matrices are applied in such a way that the precoding matrix-based channel estimation is correct, then the resulting antenna patterns will not have equal energy and precoding matrix selection via feedback from the UE will not be optimal. In the selection of the precoding matrices in the 3GPP specification, it was assumed that the energy of the antenna pattern is proportional to the energy of the precoding matrix. However, without normalization of the antenna patterns, it can be shown that for some precoding matrices, the energy of the resulting antenna pattern is significantly greater than the energy of the precoding matrix. Conversely, for other precoding matrices, the energy of the resulting antenna pattern is less than the energy of the precoding matrix.
In 3GPP, the current method used to estimate the channel gain for the data assumes that no re-scaling of the antenna pattern is necessary to maintain unit energy for all precoding matrix indicators. If the data symbols are transmitted with equal energy for all precoding matrices and if no PMI-based renormalization is performed at the UE, the precoding matrix indicator/cell-specific reference symbol (PMI/CRS)-based channel estimate will be in error. In order to compute the optimal PMI-channel quality indicator (CQI) pair, the UE must be able to compute the complex channel that would result from the application of a given PMI. With the current model, the UE does not renormalize the pattern gain for each PMI and thus the corresponding channel gain estimate used to determine the CQI will erroneous if the data symbols are transmitted with equal energy. As a result, the wrong PMI-CQI pair may be sent to the UE. Further, even if the correct PMI is chosen, the corresponding CQI may be in error. The problems described above can be expected to be most significant when the eNB antenna array is closely spaced (e.g., half-wavelength spaced arrays). The normalization issue is less significant with diversity-spaced arrays but may still be problematic.
Furthermore, an array of antenna elements can be used to reduce the power needed to transmit data from a transmitter to a receiver relative to the power needed to transmit the data with a single element of the array. This reduction in transmit power is due to the ability of the antenna array to focus the radiated power in the direction of the intended receiver. A further benefit of the antenna array is that the reduction in transmit power results in reduced interference for receivers not in the direction of the targeted receiver. Because of these benefits, antenna arrays are supported in multiple wireless communication standards, including the IEEE 802.11n, 802.11ac, 802.11ad specifications, the 3GPP HSPA and LTE specifications, and the 802.16 specifications.
In the 3GPP LTE specifications, antenna precoding matrices are defined which can be used for beamforming For an antenna array with M elements, the antenna precoders have dimension M×1. For multi-layer transmissions with K layers, the antenna precoders have dimension M×K, where the i-th column of the matrix is used for the i-th transmission layer. Each of the precoding matrices have the property that the Frobenius norm of each column of the matrix is equal to unity. As used in the 3GPP specification, the receiver selects the “best” precoder and signals this precoder back to the transmitter, where the best precoder is that which maximizes a performance metric such as the signal-to-interference plus noise ratio and/or the link throughput. In order to enable the receiver to evaluate the precoders, reference symbols are transmitted which can be used by the receiver to estimate the channel between each of the antenna array elements and the receiver. The receiver then computes the inner product of the precoder with the conjugate of the channel estimate in order to determine the channel that would be observed by the receiver if this precoder were to be applied.
From a system perspective, this precoder selection methodology is optimal in that it maximizes the performance metric, signal-to-interference plus noise ratio or throughput, for a fixed amount of transmit power. However, there is a problem that occurs if there is significant coupling of the transmit antennas. In particular, the transmitted power can vary significantly (by several dB) over the set of precoders even if all of the precoders have equal Frobenius norm. The degree of transmit power variation over the set of precoders will depend on multiple factors including the mutual coupling between the antenna elements and the circuitry used to implement the precoders and drive the antenna array. Unfortunately, present systems do not take these factors into account for precoder selection.
Thus, there is a need for a method and apparatus for optimizing antenna precoder selection with coupled antennas.